The partition is a set of integers \(\lambda =(\lambda _1,\dots ,\lambda _\ell )\) , where
\(\lambda _1 \ge \cdots \lambda _\ell > 0\)  and \(\lambda _i\)  are called parts of \(\lambda \) .
The sum of the parts is called the weight of \(\lambda \)  and is usually denoted as \(|\lambda |\) .
There is a well-known notion of Young diagrams \(\lambda \)  whose row lengths are equal to parts of \(\lambda \) .
We accept the agreement as in [1]}.
Let us denote the horizontal lengths of the part of the strings that starts at the \(ii\)  node (and does
not include it) and goes to the right as \(\alpha _i\) , and the vertical part of the column that starts at
(not including) the same node and goes down we denote \(\beta _i\) . In Frobenius coordinates, \(\lambda \)  is written
as \((\alpha |\beta )=(\alpha _1,\dots ,\alpha _k|\beta _1,\dots ,\beta _k)\) , where \(k\)  is the number of nodes on
the main diagonal of the Young diagram, see [1]} for details.
